# What is Charles’s law?

## Charles Law

Interestingly enough , many **different substances** will **behave** exactly the **same** . The accepted explanation, **James Clerk Maxwell** raised around 1860, is the amount of space occupied by a **gas** purely it depends on the **movement** of **molecules** of gas. Under normal conditions, gas molecules are very far from their neighbors, and they are so small that their own volume is negligible. The **law Charles** is a **gas law** which states that gases **expand** when **heated** . The law is also known as the**law of volumes** .

Charles’s law is a law that tells us that when the amount of **gas** and **pressure** are kept **constant** , the **ratio** between the **volume** and the **temperature** will always have the **same value** .

- What is Charles’s law?
- History
- Who proposed it
- Statement of Charles’s Law
- Formula
- Experiments
- Charles Law Applications
- Importance
- Examples

## What is Charles’s law?

Charles’s law is one of the laws that is related to **gases** . It consists of the **relationship** that exists between the **volume** and the **temperature** of a certain amount of ideal gas, which is maintained at a **constant pressure** , by means of a constant of **proportionality** that is applied directly. Jacques Charles says that for a given sum of gas at constant pressure, as the **temperature** increases , the volume of the **gas increases** and as the **temperature ****decreases** , the **volume of the gas ****decreases** because the temperature is directly related to the energy of the **movement** of the gas molecules. So, for a certain amount of gas at a given pressure, there will be a higher **speed** of the molecules and a higher **volume** of the gas.

## History

Charles’s Law was promulgated by Jacques Alexandre Charles, a renowned physicist and chemist of French origin. He was a professor of physics at the Conservatory of Arts and Crafts in Paris and with the Robert brothers, he built the first hydrogen-powered balloon. In 1787 he discovered the relationship that existed between the volume and the temperature of a gas that was under constant pressure. In 1802 he published his results, which became known as the *“Charles and Gay-Lussac law* . *“*

## Who proposed it

The law takes its name from the French scientist and inventor **Jacques Charles** , who formulated it in the **1780s** . The ironic part of the story is that Charles never published the work for which he is remembered, nor was he the first or the last to make this discovery. In fact, **Guillaume ****Amontons** had done the same kinds of experiments 100 years earlier, and it was **Joseph Gay-Lussac** in 1808 who made the **definitive measurements** and **published results** showing that every gas he tested obeyed this generalization.

## Statement of Charles’s Law

Charles’s law establishes the following postulate: *“At constant pressure , the volume that a gas sample occupies is directly proportional to the absolute temperatures that it supports”*

## Formula

According to the statement of the law, it can be expressed mathematically as follows:

**V _{1} T _{2} = V _{2} T _{1}**

Where :

- V = is used to represent
**Volume**. - T = with this letter we represent the
**Temperature**

## Experiments

On a cold day when you go out with a **helium** balloon the balloon falls apart. But when it is returned to the **warm** temperature , the balloon will return to its **original shape** . According to Charles’s law, this situation occurs because a **gas** , in this case helium, takes up more **space** when it is **hot** .

A **torch** that is used to heat the air **molecules** inside the balloon, they move faster and **disperse** into **space** . The gas inside the balloon takes up more **space** , becoming less **dense** than the surrounding air. So the hot air inside the balloon rises due to its reduced density and makes the balloon float.

**Pop-up** thermometers work on Charles’s law. The thermometer is placed in the **turkey** and as the **temperature** increases and the turkey is cooked, the **air** in the **thermometer** is **expanded** to blow the plunger. The thermometer is calibrated so when it reaches the **correct ****internal temperature** , the lid of the thermometer pops off, indicating that the turkey is done.

When playing **ping pong** , the ball may be **dented** . If **heated ****gently water** while stirring and the ball is placed inside, the air inside the ball will **expand** as it is **heated** . The expanding air will push the **dent** and restore the **roundness** of the ball.

## Charles Law Applications

Charles’s law can be used in the following applications:

- Hot air balloons
- Airbags
- Pressure cooker.

## Importance

Its importance lies in the fact that according to this law, gases **expand** when **heated** . Since the mass of the gas remains the same, the number of **molecules** per **unit** volume **decreases** as it is heated. In other words, it explains that **hot air** is **less dense** than cold air. This allows **hot** air balloons to rise, displacing cooler air in the **atmosphere** .

## Examples

An example of Charles’s law already solved is the following:

**At 1.5 atmospheres and 25 ° C the volume of a gas is 600 cm3, if the pressure remains unchanged, what will the volume of the gas be at 20 ° C?**

**First step** : the **data** given in the statement must be **identified**

**P _{1}** = 1.5 atm (cte)

**T _{1}** = 25 ° C

**V _{1}** = 600 cm3

**T _{2}** = 20 ° C

**Second step:** know what the **unknown is** .

V _{2} =?

**Third step** : we must solve for V _{2 from the expression: V 1 · T 2 = V 2 · T 1 , thus:}

V _{2} = V _{1} T _{2}

**Fourth step:** transform ° C to K, as follows:

T _{1} : K = ° C + 273 T _{2} : K = ° C + 273

K = 25 + 273 = 298 K K = 20 + 273 = 293 K

Finally the **values** are **substituted** and the **mathematical calculation** is carried out .

V _{2} = 600 cm ^{3} . 293K

298K

The **units** (Kelvin) are canceled and the **result** is obtained : **V _{2} = 589.93 cm ^{3}**